Calderon-Zygmund operators with variable kernels acting on weak Musielak-Orlicz Hardy spaces

摘要

Let Φ : R~n × [0, ∞) → [0, ∞) satisfy that Φ(x,·) is an Orlicz function for any given x∈R~n, and Φ(·,t) is a Muckenhoupt A_∞ weight uniformly in t∈(0, ∞). The weak Musielak-Orlicz Hardy space WH~Φ(R~n) is defined to be the set of all tempered distributions such that their grand maximal functions belong to the weak Musielak-Orlicz space WL~Φ(R~n). In this paper, we discuss the boundedness of the Calderon-Zygmund operator with variable kernel from WH~Φ(R~n) to WL~Φ(R~n). These results are new even for the classical weighted weak Hardy space and probably new for the classical weak Hardy space.